1. Gravitational Wave Detection
Introduction to
Gravitational Wave Detection
Ronald W. Hellings
Montana State University
PTA Workshop
Penn State
7/20/05

2. What is a gravitational wave?
space
A 2-D analogy
motion in this
dimension is
meaningless
2 free masses
The masses track
each other with lasers

3. The gravitational wave is a wave of curvature
each slice is a section of
an arc of constant radius

5. As a gravitational wave passes through the space...
the free masses remain fixed at their coordinate points
while the distance between them

6. increases due to the extra space in the curvature wave.
The laser signal has to cover more distance and is delayed

7. Why are gravitational waves called “a strain in space”?
points that are close have
little space injected
between them
points that are
further away have more
space injected between them

8. Quadrupole Gravitational Waves
a ring of free
test masses h+
less space
more space

9. Quadrupole Gravitational Waves
a ring of free
test masses h

10. Let’s do the math

11. Geometry elliptical polarization plane wave polarization angle
polarization
angle
plane wave
propagation
vector s
pulsar
Earth

12. The Gravitational Wave Metric Tensor
e.g. choose the z-axis along and the x-axis so  = 0.
Then

13. The path of the radio signal from the pulsar to the Earth is
a null path, so
Approximate
and integrate
where

14. hij is a wave, so
reception occurs at t = t, x = 0
emission occurs at t = t  s, so
The change in distance is proportional to
the integral of the wave amplitude.

15. So let’s get an observable that is proportional to the wave
Gravitational waves are proportional to the time
derivative of pulsar arrival time residuals.
But...
in the long wavelength limit (s<),
and or
LIGO
Low band of LISA

16. The Gravitational Wave Spectrum
Type
Range
Run Time
Sources
Instrument
10 Hz 
1000 Hz
compact
stars
bars,
LIGOs HF
one per day
0.1 Hz 
10Hz
one per
a few days
MAGGIE,
lunar LIGO MF ?
10 mHz 
10 mHz
binaries
SMBHs LF
one per year
LISA
1 nHz 
10 mHz
once in a
lifetime
cosmic
astrophysics
VLF
PTA
10 nHz 
0 Hz
snapshots
only
cosmic
structure
COBE, MAP
Planck, etc.
ULF

17. The Gravitational Wave Spectrum
Type
Range
Run Time
Sources
Instrument
10 Hz 
1000 Hz
compact
stars
bars,
LIGOs HF
Long wavelength limit
one per day
0.1 Hz 
10Hz
one per
a few days
MAGGIE,
lunar LIGO MF
Long and short regimes ?
10 mHz 
10 mHz
binaries
SMBHs LF
Long and short regimes
one per year
LISA
1 nHz 
10 mHz
once in a
lifetime
cosmic
astrophysics
Short wavelength only
VLF
PTA
10 nHz 
0 Hz
snapshots
only
cosmic
structure
COBE, MAP
Planck, etc.
ULF

18. The Pulsar Limit
Every pulsar in every direction has correlated timing
noise due to this term. This allows a weighted correlation
analysis to optimally use data from multiple pulsars.
~1000 years
now

19. The correlated part of the timing noise
For the nth pulsar in the direction sn, this may be written
(This generalizes the result of Hellings & Downs, 1983,
which assumed plane-polarized gravitational waves.)

20. The cross-correlation of data from 2 pulsars will produce
If are isotropic, and uncorrelated, then
where
But should be uncorrelated?
IT DEPENDS ON THE SOURCE!

21. Needs Calculation of for plane polarization  done
Calculation of and for general polarization
Thought on sources of stochastic gravitational background